Fractal Dimensions of the Hydrodynamic Modes of Diffusion

Details Fractal Dimensions of the Hydrodynamic Modes of Diffusion Fractal Dimensions of the Hydrodynamic Modes of Diffusion

2000-07-10

arxiv.org/abs/nlin/0007008v1

Nonlinear Sciences

Chaotic Dynamics

20 pages, 6 figures, submitted to Nonlinearity

Scientific paper

10.1088/0951-7715/14/2/309

We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the hydrodynamic modes of diffusion form fractal curves in the complex plane, with a Hausdorff dimension larger than one. In the limit of vanishing wavenumber, we derive a simple expression of the diffusion coefficient in terms of this Hausdorff dimension and the positive Lyapunov exponent of the chaotic model.

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